Table 1.

Field error values from Eq. (6) for the mid-surface between gray and white matter.

Error types and their percentage values	SimNIBS Ernie model (%)	1:4 Uniform Refinement	1:16 Uniform Refinement
${\mathit{Error}}_{\mathit{total}}$ for entire midsurface/SimNIBS FEM	27.1	–	–
${\mathit{Error}}_{\mathit{total}}$ for entire midsurface/iterative BEM-FMM	14.7	1.7%	0.5%
${\mathit{Error}}_{\mathit{total}}$ for entire midsurface/BEM-FMM LU	14.7	–	–
${\mathit{Error}}_{\mathit{total}}$ for 4 cm ROI under coil/SimNIBS FEM	25.0	–	–
${\mathit{Error}}_{\mathit{total}}$ for 4 cm ROI under coil/iterative BEM-FMM	3.3	0.4%	0.1%
${\mathit{Error}}_{\mathit{total}}$ for 4 cm ROI under coil/BEM-FMM LU	3.3	–	–
${\mathit{Error}}_{\mathit{mag}}$ for entire midsurface /SimNIBS FEM	17.7	–	–
${\mathit{Error}}_{\mathit{mag}}$ for entire midsurface/iterative BEM-FMM	4.9	0.6%	0.2%
${\mathit{Error}}_{\mathit{mag}}$ for entire midsurface/BEM-FMM LU	4.9	–	–
${\mathit{Error}}_{\mathit{mag}}$ for 4 cm ROI under coil/SimNIBS FEM	5.7
${\mathit{Error}}_{\mathit{mag}}$ for 4 cm ROI under coil/iterative BEM-FMM	1.6	0.2%	0.06%
${\mathit{Error}}_{\mathit{mag}}$ for 4 cm ROI under coil/BEM-FMM LU	1.6	–	–

The results for midsurface nodes are reported, which are nearly undistinguishable (difference of 0.1% or less) from the results for centers of the midsurface facets. The default Ernie model of the SimNIBS v3.2.6 FEM software with the default headreco segmentation and the default coil type/position is tested. Three solutions are considered: the default SimNIBS FEM solution, the iterative BEM-FMM solution, and the new BEM-FMM LU solution. When an outlier removal with 0.1% of the largest local errors being removed was applied, the total field error from the second row of Table 1 reduced from 27.1 to 26.2% and the ROI field error from the fifth row of Table 1 reduced from 25.0 to 22.8%